We show that the Owen value for TU games with a cooperation structure extends the Shapley value in a consistent way. In particular, the Shapley value is the expected Owen value for all symmetric distributions on the partitions of the player set. Similar extensions of the Banzhaf value do not show this property. Journal of Economic Literature Classification Number: C71.

Shapley operators are the dynamic programming operators of zero-sum stochastic games, they can be characterized as order-preserving maps commuting with the addition of a constant. We study a subclass of Shapley operators which are characterized by the property of commuting with the multiplication by a positive constant. We call them paymentfree, as they arise in the study of recursive games, in...

In allocation problems, a given set of goods are assigned to agents in such a way that the social welfare is maximised, that is, the largest possible global worth is achieved. When goods are indivisible, it is possible to use money compensation to perform a fair allocation taking into account the actual contribution of all agents to the social welfare. Coalitional games provide a formal mathema...

In this paper cost sharing problems are considered. We focus on problems on a rooted tree, we call these problems cost-tree problems, and on the induced transferable utility cooperative games, we call these games irrigation games. A formal notion of irrigation games is introduced, and the characterization of the class of these games is provided. The well-known class of airport games (Littlechil...

One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities (partition-function games). When externalities are present, not only can a player’s marginal contribution—a central notion to the Shapley value—be defined in a variety of ways, but it is also not obvious which axiomatization should be used. Consequently, a number of authors e...

This paper presents a collection of four different classes of weighted Shapley levels values. All classes contain generalisations of the weighted Shapley values to cooperative games with a level structure. The first class is an upgrade of the weighted Shapley levels value in Gómez-Rúa and Vidal-Puga (2011), who use the size of components as weights. The following classes contain payoff vectors ...

We examine the characterization of the Shapley value that was introduced by Young and refined later by Neyman. A new proof of this axioma-tization is given and as an illustration of the new proof it is demonstrated that the axioms under consideration characterize the Shapley value on various well-known classes of T U games.

We study the complexity of the following problem: Given two weighted voting games G′ and G′′ that each contain a player p, in which of these games is p’s power index value higher? We study this problem with respect to both the Shapley-Shubik power index [SS54] and the Banzhaf power index [Ban65, DS79]. Our main result is that for both of these power indices the problem is complete for probabili...

We propose the study of computing the Shapley value for a new class of cooperative games that we call budgeted games, and investigate in particular knapsack budgeted games, a version modeled after the classical knapsack problem. In these games, the “value” of a set S of agents is determined only by a critical subset T ⊆ S of the agents and not the entirety of S due to a budget constraint that l...

In [6] we computed the edge Folkman number F (3, 4; 8) = 16. There we used and announced without proof that in any blue-red coloring of the edges of the graph K1 +C5 +C5 + C5 there is either a blue 3-clique or red 4-clique. In this paper we give a detailed proof of this fact.